That kind of tax would constitute a massive increase in effective tax rates on the middle class and poor, even as it amounted to a massive tax cut for the rich. That's a good idea if you think the pressing problem in America today is too little income inequality and wealth stratification. If you think life's gotten too darn rough on the rich and too cushy for the poor, then it's a great change. If, on the other hand, you think we're in the opposite situation, it'll make things worse.
Here's a way to think about the numbers.
https://www.taxpolicycenter.org/statistics/historical-average-federal-tax-rates-all-households
That's a bit dated, but take a look at 2015. As you can see, in the average total federal tax rate for everyone (the effective federal tax rate) was 21.1%. So, if you could get perfect tax collection (no write-offs, no dodging) you'd need to set the rate at 21.1% to collect the same revenues. Now, look what that means for each group.
For those in the bottom 20%, it means their effective tax rate would be 14 times as high as now. For those in the next 20% (the lower-middle class), taxes would jump to over twice what they currently pay. For the next 20% (the middle-middle class), the tax hit would be 50% higher than it currently is. For the next 20% (the upper-middle class), it would still be a rise from 17.9% to 21.1%, which is an increase of about 18% in what their tax bill would be. So, there you have 80% of the population experience the change you're calling for as a giant tax hike. Only the upper class would be better off.
For the top 1%-ers, though, it would be a huge windfall, dropping their effective tax rates from 33.3% to 21.1%, which is a decline of about 37% in what they'll owe. So, would you really support a 21.1% flat tax for everyone?
It makes sense the very rich keep pushing this notion of a Flat Tax. If you're Steve Forbes, handed a massive fortune by your father, it's a great idea. For the rest of us, though, it really sucks. The only way it wouldn't absolutely devestate the poor and middle class is to move to a more European-style government system, where the state provides enough of life's basics that it's not a great hardship for people to have little take-home pay (e.g., "free" healthcare, childcare, college, and heavily subsidized public transit, etc.)
That said, we could move to a progressive simplified tax -- that is, keep a progressive structure even as we eliminate most or all write-offs. The vast majority of complexity in the tax code has nothing to do with the brackets, so eliminating those doesn't really help anything. Rather, it's all the special rules to benefit politically useful constituencies (e.g., special tax rules to benefit veterans, farmers, small businesses, churches, and so on).